Measurement of highly reflective surface shape using wavelength tuning Fizeau interferometer and polynomial window function |
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| Affiliation: | 1. State Key Lab of Clean Energy Utilization, Zhejiang University, Hangzhou 310027, China;2. UMR 6614/CORIA, Normandie Université, CNRS, Université et INSA de Rouen, bp12 76801 Saint Etienne du Rouvray, France;1. College of Electronics and Information Engineering, Sichuan University, Chengdu, Sichuan Province 610064, China;2. Centre for Optical and Laser Engineering, School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore 639798, Singapore;3. Beijing Key Lab of Spatial Information Integration and 3S Application, Peking University, Beijing 100871, China;1. Department of Radiation Protection and Radioactive Waste Safety, Korea Institute of Nuclear Safety, 62 Gwahak-ro, Yuseong-gu, Daejeon 34142, Republic of Korea;2. School of Environmental Science and Engineering, Gwangju Institute of Science and Technology, 1 Oryong-dong, Buk-gu, 500-712 Gwangju, Republic of Korea;3. Research Center for Membranes, Korea Research Institute of Chemical Technology (KRICT), Daejeon 305-600, Republic of Korea;1. Faculty of Science, Engineering, Jiangsu University, Zhenjiang, 212013, China;2. School of Mechanical Engineering, Jiangsu University, Zhenjiang, 212013, China;1. Department of Physics and Institute of Optics, Ningbo University, Ningbo 315211, China;2. Graduate School at Shenzhen, Tsinghua University, Shenzhen 518055, China |
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| Abstract: | In this study, a 5N ? 4 phase shifting algorithm comprising a polynomial window function and a discrete Fourier transform is developed to measure interferometrically the surface shape of a silicon wafer, with suppression of the coupling errors between the higher harmonics and the phase shift error. A new polynomial window function is derived on the basis of the characteristic polynomial theory by locating five multiple roots on the characteristic diagram. The characteristics of the 5N ? 4 algorithm are estimated with respect to the Fourier representation in the frequency domain. The phase error of the measurements performed using the 5N ? 4 algorithm is discussed and compared with those of measurements obtained using other conventional phase shifting algorithms. Finally, the surface shape of a 4-in. silicon wafer is measured using the 5N ? 4 algorithm and a wavelength tuning Fizeau interferometer. The accuracy of the measurement is discussed by comparing the amplitudes of the crosstalk noise calculated by other algorithms. The uncertainty of the entire measurement was 34 nm, better than that of any other conventional phase shifting algorithms. |
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| Keywords: | Interferometry Surface shape Phase shifting algorithm Phase error |
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